Method for determining positions of targets by bistatic measurements using signals scatttered by the targets

ABSTRACT

The present invention relates to a method for determining the positions of targets by bistatic measurements using signals scattered by the targets. Also the velocities of the targets can be determined. The range of the transmitters is selected so that a target at an arbitrary point can be measured by scattering in the target by at least four cooperating measuring facilities. First the targets are associated. This occurs by calculating, in two independent ways, two sets of sums of distances between transmission points and targets and, respectively, targets and reception points. Subsequently, said two sums are sorted with respect to distance, compared with each other, and the sums that correspond with each other, while considering a margin of error that has been determined in advance, are stated to correspond to conceivable targets. The association of targets is improved and completed by corresponding calculations being carried out for Doppler velocities. Finally, the positions of the targets are calculated from a system of equations for the bistatically measured distances.

The present invention relates to a method for determining positions oftargets by bistatic measurements using signals scattered by the targets.Also the velocities of the targets can be determined. The methodcomprises a rapid bistatic association method which is suitable for, forinstance, a network of radar stations in the manner of MSR (AssociativeAperture Synthesis Radar) although there may be further fields ofapplication. AASR is described, inter alia, in Swedish Patent 0101661-7,which is herewith incorporated by reference. In the following, thedescription will be concentrated on the new method of associating bybistatic measurements only.

First the fundamental problem that is solved by the invention will bepresented. N_(s) stations (for instance radar stations) are imagined tobe set out in the space (R³). The stations are designated s_(j), j=1, .. . N_(s) and their position vectors are designated p_(j), j=1, . . .N_(s). In addition to the stations, there are also N_(t) moving targetswhich are to be detected. They are designated t_(i), i=1, . . . N_(t)and have corresponding time-dependent position vectors r_(i)=r_(i)(t),i=1, . . . N_(t).

Each station is capable of measuring distances (up to a certain maximumdistance) and radial speed for each target. Thus, the station s_(j),1≦j≦N_(s) will, at a certain point of time, measured _(j)(k)=|r _(k) −p _(j) |, k=1, 2, . . . N _(dj) ≦N _(t)v _(j)(k)=(d/dt)|r _(k) −p _(j) |, k=1, 2, . . . N _(dj) ≦N _(t)

For stations that are sufficiently close to each other, also bistaticmeasurement information is obtained, i.e. transmitting from one stationand registration at another. For the pair of stations (s_(i), s_(j)) itmeans that the following is registeredd _(ij)(k)=|r _(k) −p _(i) |+|r _(k) −p _(j) |=d _(i)(k)+d _(j)(k), k=1,2, . . . N _(dij) ≦N _(t)v _(ij)(k)=(d/dt)|r _(k) −p _(i)|+(d/dt)|r _(k) −p _(i) |=v _(i)(k)+v_(j)(k), k=1, 2, N _(dij) ≦N _(t)

It is to be noted that with these designations, d_(ii)(k)=2d_(i)(k),v_(ii)(k)=2v_(i)(k), i=1,2, . . . , k=1,2, . . . .

For each sensor (monostatic or bistatic geometry) targets are thusregistered in respect of distance and Doppler. It is a priori notpossible to know which registration from one sensor is associated with acertain registration from another sensor, i.e. originating from the sametarget. If registrations from different sensors are paired incorrectly,false targets, ghost targets, arise. The problem of association is todiscriminate, among all conceivable possibilities of combining sensordata, corresponding to conceivable target candidates, between correctcombinations (targets) and false combinations (ghosts).

The maybe most straight-forward method is to consider three neighbouringstations and their monostatic registrations, which for the sake ofsimplicity are assumed to be N in number. These measurements can becombined in N³ ways where each combination corresponds to a targetposition which is determined up to reflection in the plane containingthe three stations. (Certain combinations can be incompatible,corresponding to false candidates.) These ˜N³ candidates can then one byone be compared with the bistatic measurements and either be rejected oraccepted. The problem of such a method is that it will be very slow ifthe number of targets, N, is large. For this reason, more efficientassociation algorithms have been developed.

Each target is to be determined in respect of position as well asvelocity, i.e. they are to be positioned in a six-dimensional statespace. The number of cells in the state space can be very large (˜10¹⁸),which means that traditional projection methods will be irretrievablyslow.

The above Swedish Patent 0101661-7 discloses a method of attacking theproblem of association by designing a sensor network so that each targetis registered by many sensors (monostatic and bistatic), i.e. a highdegree of redundancy is obtained in the system. Then the state space isdivided into a manageable number of relatively large cells.

If the cells are just large enough, it will be possible to reject manyof them, i.e. they cannot contain any targets, for the followingreasons. If the cell contains a target, all (or almost all) of thepossible sensors that can register targets in the current cell, willindicate such a registration. On the other hand, if the cell is empty,some sensors, and yet not too many, will still indicate registrations(from other targets) that are compatible with the cell in question.Owing to redundancy, a sufficient number of sensors will indicate thecell as empty, and it can be rejected. When the number of cells is thusreduced, the surviving cells are divided into smaller cells and theprocess is repeated. The process is repeated until the cells in thestate space have reached the desired size. As the cells are becomingsmaller, fewer and fewer ghost targets will survive, so that, wheninterrupting the process, practically only real targets are left. Whatspeaks in favour of this method is that it uses (but also requires) theredundancy of the sensor network. However, it is not yet quite clear howrapid the method may eventually be.

An alternative method is disclosed in Swedish Patent 0101662-5, which isherewith incorporated by reference, and implies that use is made ofcertain symmetries of the combination sensors—measurement data. Giventwo stations, the two monostatic measurements, together with thebistatic measurement, will share a symmetry, viz. that the threemeasuring geometries are all insensitive to rotation of the targetsabout the axis extending through the two stations. This means that it ispossible to make an initial rapid screening of the candidates and deletea large number of false associations (ghosts). The subsequent finalassociation will then be significantly more rapid. A drawback, however,is that the monostatic measurements will be important, which may bedisadvantageous in connection with reconnaissance of stealth targets.

The present method according to the invention is based on using a rapidmethod where only bistatic measurements are utilised. Furthermore themethod manages a certain dropout of sensors in a better way than themethod that has been discussed directly above. The method solves thecurrent problem of association by being designed in the manner as isevident from the independent claim. Advantageous embodiments of theinvention are defined in the remaining claims.

Before a more detailed description of the invention, first a multistaticnetwork of ground radar stations will be contemplated, in which eachradar station transmits radar pulses that are scattered towards flyingtargets and are then received by the surrounding stations. There willthen be a situation involving a large number of bistatic measurements(i.e. the transmitting and the receiving station are located indifferent positions) and also monostatic measurements which, however,are not used in the invention. The bistatic measurements containinformation about the total distance transmitter-target-receiver andcorresponding Doppler information. A coherent air situation image isthen to be created from all these measurements. This problem, theproblem of association, is non-trivial if there are a large number oftargets.

For intuitive understanding of the invention, a simple case is takeninto consideration, involving only one target, m₁, and four stations s₁,s₂, s₃, s₄. Now assume that the measurements d₁₂, d₃₄, d₁₃, d₂₄ areperformed, where d_(ij) means the total distance s_(i)−m₁−s_(j). It willbe appreciated that d₁₂+d₃₄=d₁₃+d₂₄ must be the case since bothexpressions mean the total distance from the target to the fourstations.

If there are now N targets instead, the above observation can be used tocorrectly associate data in the following manner. All conceivablecombinations of data of the type d₁₂ and d₃₄ are formed; they will be N²in number. In the same way, N² combinations of data of the type d₁₃ andd₂₄ are formed. These combinations are sorted and compared, and onlysums from the two amounts that are equal (within a given tolerance) cancorrespond to real targets. The same discussion can be used about theDoppler velocities which thus give a further screening. In this way,quick and easy association of measurement data can be effected.

In general, the transmitters and receivers must be positioned and therange of the transmitters must be chosen so that a target at anarbitrary point within the position space can be measured via scatteringin the target of at least four cooperating bistatic pairs oftransmitters and receivers. The number of transmitters and receivers canbe large. At least four such cooperating pairs are selected among thesebistatic pairs to perform the association and the determination of thedistance.

Below follows a more systematic presentation of the calculations. Inorder to obtain a simple description, the following (non-critical)assumptions are made. Assume that there are four stations and N targets,which all are seen by all sensors (monostatic as well as bistatic).

Input data is thus (monostatic measurements)d _(j)(k)=|r _(k) −p _(j) |, k=1, 2, . . . N, j=1,2,3,4v _(j)(k)=(d/dt)|r _(k) −p _(j) |, k=1, 2, . . . N, j=1,2,3,4and (bistatic measurements)d _(ij)(k)=|r _(k) −p _(i) |+|r _(k) −p _(i) |=d _(i)(k)+d _(j)(k), k=1,2, . . . N, j=1,2,3,4v _(ij)(k)=(d/dt)|r _(k) −p _(i)|+(d/dt)|r _(k) −p _(j) |=v _(i)(k)+v_(j)(k), k=1, 2, . . . N, j=1,2,3,4where i=j in the bistatic case corresponds to monostatic measurements,i.e. i≠j can be assumed if desirable.

It is to be noted that, for instance, for station j, with the monostaticmeasurement d_(j)(k), k=1,2, . . . N, it is not possible to know whichmeasurement belongs to a certain target, i.e. the measurements are to beregarded as a set which is as a suggestion sorted according to distance.In this way, there is no connection between a certain index k whichbelongs to two different sensor registrations.

The method is now based on the following observation: For eachregistered target (not candidate, but real target) there must be a k, ak′, an l and an l′, all between 1 and N so thatd₁₂(k)+d₃₄(l)=d₁₃(k′)+d₂₄(l′)

For the same k, k′, l, l′, the following is also applicablev₁₂(k)+v₃₄(l)=v₁₃(k′)+v₂₄(l′)

The reason is that if the target has the space vector r_(t), it isapplicable for the target thatd₁₂(k)+d₃₄(l)=|r_(t)−p₁|+|r_(t)−p₂|+|r_(t)−p₃|+|r_(t)−p₄|and in the same way thatd₁₃(k)+d₂₄(l)=|r_(t)−p₁|+|r_(t)−p₃|+|r_(t)−p₂|+|r_(t)−p₄|so that they are equal. The argument for the velocities is identical.The suggested method now is as follows.Step 1. Form the N² sumsd ₁₂(k)+d ₃₄(l), 1≦l, k≦NSort them according to the total distance and designate themd ₁₂₊₃₄(m), 1≦m≦N ²Step 2. Proceed in the same way withd ₁₃(k′)+d ₂₄(l′), 1≦l′, k′≦Nso that the following will also be obtained (sorted)d ₁₃₊₂₄(m′), 1≦m′≦N ²Step 3. Associate targets from {d₁₂₊₃₄(m)}_(m=1,2 . . . N) ₂ withtargets from {d₁₃₊₂₄(m′)}_(m′=1,2 . . . N) ₂ if|d ₁₂₊₃₄(m)−d ₁₃₊₂₄(m′)|<suitable toleranceStep 4. Investigate, and keep associated targets if they also satisfy|v ₁₂₊₃₄(m)−v ₁₃₊₂₄(m′)|<suitable tolerance

“Suitable tolerance” in Step 3 is determined, inter alia, by thetransmitted signal bandwidth, the purpose of the processing andhypotheses about size and number of the targets. Usually it is fromabout one meter to some twenty or thirty meters. Correspondingly,“suitable tolerance” in Step 4 is usually a few meters/second.

To establish that this really results in a rapid method, the followingrough estimate may be used. Assume that there are many targets so thatthey are of the same magnitude as the number of distance bins and thenumber of Doppler bins. This common number is again designated N. It maythen be estimated that, since the total number of cells (=number ofdistance bins by the number of Doppler bins) is the same as the numberof candidates in for instance {d₁₂₊₃₄(m)}_(m=1,2 . . . N) ₂ , each suchcandidate will be paired with typically a false candidate from{d₁₃₊₂₄(m′)}_(m′=1,2 . . . N) ₂ . The number of candidates according tothe above procedure thus is ˜N² (fewer with fewer targets), which is agreat reduction compared with N³. Further processing can then take placeby comparing with the remaining bistatic geometry{d₁₄₊₂₃(m″)}_(m″=1,2 . . . N) ₂ the mono static measurements ormeasurements involving other stations.

It is also to be noted that it is possible to involve{d₁₄₊₂₃(m″)}_(m″−1,2 . . . N) ₂ from the beginning. This gives apossibility of having a redundancy, i.e. a possibility of managing acertain dropout in registrations, in the following way. The conditionthat |d₁₂₊₃₄(m)−d₁₃₊₂₄(m′)|<“suitable tolerance” can be seen as if bothd₁₂₊₃₄(m) and d₁₃₊₂₄(m′) are to be close to a certain given value. Byrequiring instead that two of d₁₂₊₃₄(m), d₁₃₊₂₄(m′) and d₁₄₊₂₃(m″)should be close to the indicated value (for some values of m, m′ and m″)there will still be a discrimination between false candidates (ghosts)and targets. However, it may be accepted that one of the measurementsdrops out.

The calculations in their entirety require O(N² log N) operations, andthere are simple methods of really obtaining position and velocity fromthe candidates, i.e. after processing four bistatic distances are knownfor a certain candidate as follows:|r−p ₁ |+|r−p ₂ |=d ₁₂|r−p ₃ |+|r−p ₄ |=d ₃₄|r−p ₁ +|r−p ₃ |=d ₁₃|r−p ₂ |+|r−p ₄ |=d ₂₄

It is, of course, interesting to know the value of r (position of thetarget), i.e. a method of solving the above system of equations. (p_(i),i=1,2,3,4, are the known positions/position vectors of the stations andd₁₂, d₃₄, d₁₃, d₂₄ are the measured bistatic distances.) Generally seen,intersections of ellipsoids cause relatively complicated algebraicsystems of equations, but in this case the system of equations can besolved by simpler methods.

If the system of equations is regarded as a 4×4 system, it is obviousthat it is degenerated. At the same time the condition d₁₂+d₃₄=d₁₃+d₂₄guarantees that there is a parameter solution. By selecting the originof coordinates in p₄ so that |r−p₄|=|r|=r and introducing r as aparameter, the following equations are obtained|r−p ₁ |=d ₁₂ −d ₂₄ +r|r−p ₂ |=d ₂₄ −r|r−p ₃ |=d ₃₄ −r

It is here possible to square the three equations, in which case r² canbe deleted, and obtain the following (for some a,b,c,α,β,γ)r·p ₁ =ar+αr·p ₂ =br+βr·p ₁ =cr+γ

The latter system of equations can then be solved in a fairlystraight-forward way. However, there will be two different cases independence on whether {p_(i)}_(i=1,2,3) is linearly dependent or not.

The case of the velocities is similar, the following system of equationswill be obtainedû ₁ ·{overscore (v)}+û ₂ ·{overscore (v)}=v ₁₂û ₃ ·{overscore (v)}+û ₄ ·{overscore (v)}=v ₃₄û ₁ ·{overscore (v)}+û ₃ ·{overscore (v)}=v ₁₃û ₂ ·{overscore (v)}+û ₄ ·{overscore (v)}=v ₂₄where $\begin{matrix}{\begin{matrix}{{{\hat{u}}_{i} = \frac{\overset{\_}{r} - {\overset{\_}{r}}_{i}}{{\overset{\_}{r} - {\overset{\_}{r}}_{i}}}},} & {\overset{\_}{V} = \overset{\overset{.}{\_}}{r}}\end{matrix},} & {{i = 1},2,3,4.}\end{matrix}$The system of equations can be processed in the same fundamental way asthe previous system of equations.

The invention can be implemented in high-level languages which aresuitable for calculations, such as MatLab, C, Pascal, Fortran etc.

1. A method for determining positions of targets in a position spaceusing signals scattered by the targets, comprising use of a number,spread in known points in the position space, of transmitters andreceivers of electromagnetic or acoustic signals, each bistatic pair oftransmitter and receiver being referred to as a measuring facility,further comprising analysis of received signals, which includesdetermining of moments of transmission and reception according togenerally accepted principles of radar and parameterisation of receivedsignals as a function of the path of propagation between transmissionpoint and reception point, but without the conventional requirement inradar for directional information, the positions being primarilydetermined by selecting the position of the transmitters and receiversand the range of the transmitters so that a target at an arbitrary pointwithin the position space can be measured by scattering in the target byat least four cooperating measuring facilities; by selecting an evennumber of cooperating measuring facilities, however at least 4, for thedetermination; by associating targets by calculating, in two independentways, two sets of sums of distances between transmission points andtargets and, respectively, targets and reception points, based onbistatic distances, measured via the targets, for selected measuringfacilities, sorting said two sums with respect to the distance,comparing these with each other and establishing that the sums,calculated in the two different ways, which correspond with each other,while considering a margin of error that has been determined in advance,are stated to correspond to conceivable targets; and by calculating thepositions of the targets from a system of equations for the bistaticallymeasured distances, characterised by improving and completing theassociation of targets by performing calculations for bistaticallymeasured Doppler velocities, corresponding to calculations fordistances, and establishing that the sums, calculated in the twodifferent ways, which correspond with each other, while considering amargin of error that has been determined in advance, are stated tocorrespond to targets.
 2. A method as claimed in claim 1, characterisedby improving the association of targets by calculating the sum of alldistances between the targets and the transmission points and thereception points, respectively, in a third way as the sum ofbistatically measured distances via the target for measuring facilities,sorting the sum with respect to the distance, comparing this withpreviously calculated sums of distances, and establishing that the caseswhere two of the three sums, calculated in said different ways,correspond with each other, while considering a margin of error that hasbeen determined in advance, are stated to correspond to targets.
 3. Amethod as claimed in claim 1, characterised by improving the associationof targets by calculating the sum of all Doppler velocities between thetargets and the transmission points and the reception points,respectively, in a third way as the sum of bistatically measured Dopplervelocities via the target for measuring facilities, sorting the sum withrespect to Doppler velocity, comparing this with previously calculatedsums of Doppler velocities and establishing that the cases where two ofthe three sums, calculated in said different ways, correspond with eachother, while considering a margin of error that has been determined inadvance, are stated to correspond to targets.
 4. A method as claimed inclaim 2 or 3, characterised by improving the association of targets byrequiring that all three sums, calculated in said different ways,correspond with each other, while considering a margin of error that hasbeen determined in advance, for targets to be indicated.
 5. A method asclaimed in claim 4, characterised by calculating the velocities of thetargets from a system of equations for the bistatically measured Dopplervelocities.
 6. A system for determining positions of targets in aposition space using signals scattered from the targets, comprising anumber, spread in known points in the position space, of transmittersand receivers of electromagnetic or acoustic signals, each bistatic pairof transmitter and receiver being referred to as a measuring facility,further comprising analysis equipment for storing and analysing receivedsignals, which includes determining of moments of transmission andreception according to generally accepted principles of radar andparameterisation of received signals as a function of the path ofpropagation between transmission point and reception point, but withoutthe conventional requirement in radar for directional information, thepositions being primarily determined by the position of the transmittersand receivers and the range of the transmitters being selected so that atarget at an arbitrary point within the position space can be measuredby scattering in the target by at least four cooperating measuringfacilities; by the analysis equipment selecting an even number ofcooperating measuring facilities, however at least 4, for thedetermination; by the analysis equipment associating targets bycalculating, in two independent ways, two sets of sums of distancesbetween transmission points and targets and, respectively, targets andreception points, based on bistatic distances, measured via the targets,for selected measuring facilities, sorting said two sums with respect tothe distance, comparing these with each other and establishing that thesums, calculated in the two different ways, which correspond with eachother, while considering a margin of error that has been determined inadvance, are stated to correspond to conceivable targets, and by theanalysis equipment calculating the positions of the targets from asystem of equations for the bistatically measured distances,characterised in that the analysis equipment improves and completes theassociation of targets by performing calculations for bistaticallymeasured Doppler velocities, corresponding to the calculations for thedistances, and establishing that the sums, calculated in the twodifferent ways, which correspond with each other, while considering amargin of error that has been determined in advance, are stated tocorrespond to targets.
 7. A system as claimed in claim 6, characterisedin that the analysis equipment improves the association of targets bycalculating the sum of all distances between the targets and thetransmission points and the reception points, respectively, in a thirdway as the sum of bistatically measured distances via the target formeasuring facilities, sorting the sum with respect to the distance,comparing this with previously calculated sums of distances, andestablishing that the cases where two of the three sums, calculated insaid different ways, correspond with each other, while considering amargin of error that has been determined in advance, are stated tocorrespond to targets.
 8. A system as claimed in claim 6, characterisedin that the analysis equipment improves the association of targets bycalculating the sum of all Doppler velocities between the targets andthe transmission points and the reception points, respectively, in athird way as the sum of bistatically measured Doppler velocities via thetarget for measuring facilities, sorting the sum with respect to Dopplervelocity, comparing this with previously calculated sums of Dopplervelocities and establishing that the cases where two of the three sums,calculated in said different ways, correspond with each other, whileconsidering a margin of error that has been determined in advance, arestated to correspond to targets.
 9. A system as claimed in claim 7 or 8,characterised in that the analysis equipment improves the association oftargets by requiring that all three sums, calculated in said differentways, correspond with each other, while considering a margin of errorthat has been determined in advance, for targets to be indicated.
 10. Asystem as claimed in claim 9, characterised in that the analysisequipment calculates the velocities of the targets from a system ofequations for the bistatically measured Doppler velocities.
 11. A methodas claimed in claim 3, characterised by improving the association oftargets by requiring that all three sums, calculated in said differentways, correspond with each other, while considering a margin of errorthat has been determined in advance, for targets to be indicated.
 12. Asystem as claimed in claim 8, characterised in that the analysisequipment improves the association of targets by requiring that allthree sums, calculated in said different ways, correspond with eachother, while considering a margin of error that has been determined inadvance, for targets to be indicated.